Sizing Batteries – SS1 Solar Photovoltaic Installation & Maintenance Lesson Note (Third Term)

Battery sizing is the process of working out how many amp-hours (Ah) a solar battery must hold to supply the night load.

Behavioural objectives

By the end of the lesson, students should be able to:

1. Explain daily load, depth of discharge (DoD) and autonomy.
2. Calculate the night load in watt-hours (Wh) from appliance ratings and hours of use.
3. State the safe DoD for lead-acid (tubular) and lithium batteries.
4. Use the formula to calculate battery size in amp-hours (Ah).
5. Choose a battery size that is available to buy.

What do we need to know before sizing a battery?

We need three things: the daily load, the depth of discharge (DoD) and the days of autonomy.

Think of a battery as a water tank in a house.

• Daytime: the solar panels (the pump) fill the tank.
• Night-time: the appliances use the water from the tank.
• Tank too small: the water finishes before morning, so the lights go off at 2:00 AM.

What are the three key terms?

• Daily load: the energy in watt-hours (Wh) that the appliances use. It answers “how much water do we use?”
• Depth of Discharge (DoD): the part of the battery’s capacity that can be used safely. It answers “how much water can we take out without damaging the tank?”
• Autonomy: the number of days the battery can supply the load when the panels give no charge. It answers “how long should the tank last if it does not rain?”

What units and relationships are used?

How do you size a solar battery?

You size a battery in four steps: find the load, apply the DoD, choose the autonomy and calculate the Ah.

Step 1: How do you calculate the daily (night) load?

The night load is the total watt-hours (Wh) the appliances use between sunset and sunrise.

1. List every appliance that will run at night.
2. Multiply the number of appliances by the watts of each one.
3. Multiply by the hours of use.
4. Add all the results.

Worked example:

• 2 fans (60W each) for 8 hours: 120W × 8 = 960Wh.
• 5 bulbs (10W each) for 10 hours: 50W × 10 = 500Wh.
• Total night load: 960 + 500 = 1,460Wh.

The battery must hold this 1,460Wh until the sun comes up.

Step 2: What is depth of discharge (DoD)?

Depth of discharge is the percentage of a battery’s capacity that you can use without shortening its life.

• Safety rule: never empty a battery completely, because deep discharge damages it and shortens its life.
• Lead-acid (tubular) batteries: use only about 50% of the capacity. From a 100Ah battery, take out only 50Ah.
• Lithium batteries: use about 80% to 90% of the capacity safely.

Example: a night load of 1,000Wh needs a 2,000Wh lead-acid battery, so that only half of it is used.

Step 3: What is battery autonomy?

Autonomy is the number of days a battery can power the load without any charge from the sun.

• Why it matters: Nigeria has many cloudy or rainy days in July and August.
• 1 day of autonomy: if it rains all day, the batteries do not charge and the house is dark that night.
• More days of autonomy: the battery lasts through cloudy spells, but it is larger and costs more.
• Typical design: 1 to 2 days of autonomy.

To include autonomy, multiply the daily load by the number of days.

• Example: 1,460Wh × 2 days = 2,920Wh.

Step 4: What is the formula for battery size?

The battery size in amp-hours (Ah) is the number written on the battery.

Battery size (Ah) = (Total load × Days of autonomy) ÷ (Battery voltage × DoD)

Worked example 1: 1 day of autonomy

• Load: 1,460Wh
• Autonomy: 1 day
• Voltage: 12V
• DoD: 0.5 (50%)

1. Top line: 1,460 × 1 = 1,460.
2. Bottom line: 12 × 0.5 = 6.
3. Battery size: 1,460 ÷ 6 = 243.3Ah.

Worked example 2: 2 days of autonomy

1. Top line: 1,460 × 2 = 2,920.
2. Bottom line: 12 × 0.5 = 6.
3. Battery size: 2,920 ÷ 6 = 486.7Ah.

How do you choose a battery that is available to buy?

Always round up to the next available size, never down.

• Rounding up: a 243Ah result is not easy to find, so buy a 300Ah battery.
• Joining batteries: two 150Ah, 12V batteries connected in parallel give 300Ah at 12V.
• Rounding down: a smaller battery is discharged too deeply, so it wears out early.

What mistakes make batteries fail early?

• Ignoring DoD: buying a battery equal to the load, so it is emptied every night.
• Forgetting appliances: leaving out a fridge, TV or phone chargers from the load.
• Wrong hours: counting daytime hours in the night load.
• Rounding down: choosing a battery smaller than the calculated size.

Evaluation

Class activity: the “Rainy Day” planner

1. State: give the safe DoD for a lead-acid (tubular) battery and for a lithium battery.
2. The comparison: a lithium battery allows 90% DoD and a tubular battery allows 50%. Which one lets you buy a smaller battery for the same work?
3. The group task: calculate the battery size for a small shop that uses 500Wh at night, wants 2 days of autonomy, and uses a 12V battery with 50% DoD.
4. Discussion: why do many people in Nigeria complain that their batteries do not last, even when the batteries are new? (Hint: think about DoD.)

Assignment

1. Explain in your own words what autonomy means and why it matters in July and August in Nigeria.
2. A house has a night load of 800Wh. Using a 12V tubular battery with 50% DoD and 1 day of autonomy, calculate the battery size in Ah.